Paper Citation Record · LEDGER

Gradient Descent's Last Iterate is Often (slightly) Suboptimal

As of 10 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 3 inbound Pith citation observations for arXiv:2604.13870.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2604.13870 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T12:27:10.934480Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T08:04:06.432613Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-04T18:40:02.584054Z

Reference resolution

31 of 31 outbound references displayed

verified exact3
verified fuzzy26
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1646cc3f-e3e0-4919-86f6-3b5621937565 · outbound

This paper cites Acceleration by stepsize hedging: Silver stepsize schedule for smooth convex optimization.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Acceleration by stepsize hedging: Silver stepsize schedule for smooth convex optimization

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.749803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 83288431-43cb-420e-a64a-c918a27ab892 · outbound

This paper cites Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:30:23.755228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 78fc1514-2f93-44ff-9650-aa743fc22a8e · outbound

This paper cites Large-scale machine learning with stochastic gradient descent.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Large-scale machine learning with stochastic gradient descent

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.745804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e3afec09-2a2f-42b1-8f6d-d88873b3fca0 · outbound

This paper cites Last iterate convergence of incremental methods and applications in continual learning.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Last iterate convergence of incremental methods and applications in continual learning

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.727885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e47af917-3ffd-459b-8fbf-3c188a7fe3f6 · outbound

This paper cites From continual learning to sgd and back: Better rates for continual linear models.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal From continual learning to sgd and back: Better rates for continual linear models

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.694306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 391611ee-09ef-45c3-9222-b6a2be1738eb · outbound

This paper cites Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T12:30:23.751347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f3f59019-e9c8-4dfe-8b99-776c5c10c9d4 · outbound

This paper cites Deep learning, volume 1.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Deep learning, volume 1

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.686371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 016108b7-568b-47e3-990c-3df7428cbbe5 · outbound

This paper cites Sgd: General analysis and improved rates.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Sgd: General analysis and improved rates

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.690532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2f306735-9496-4208-8b5c-c8baa68f2a56 · outbound

This paper cites Accelerated objective gap and gradient norm convergence for gradient descent via long steps.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Accelerated objective gap and gradient norm convergence for gradient descent via long steps

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.698033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 77d71d06-cd3a-4775-8b4c-f509c36ab0db · outbound

This paper cites Tight analyses for non-smooth stochastic gradient descent.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Tight analyses for non-smooth stochastic gradient descent

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.705726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 778408c6-7e05-44d8-8c3b-f8ff0cca68a6 · outbound

This paper cites Introduction to online convex optimization.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Introduction to online convex optimization

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.682461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f4c96784-25c1-4ca9-9b63-400fb3a0a277 · outbound

This paper cites Beyond the regret minimization barrier: optimal algorithms for stochastic strongly-convex optimization.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Beyond the regret minimization barrier: optimal algorithms for stochastic strongly-convex optimization

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.678602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9ee75dda-e1c3-4918-91c8-c2c5b025ee1b · outbound

This paper cites Making the last iterate of sgd information theoretically optimal.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Making the last iterate of sgd information theoretically optimal

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.701888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 70db4058-cdf6-4103-b02b-5cb974803b05 · outbound

This paper cites Open problem: Anytime convergence rate of gradient descent.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Open problem: Anytime convergence rate of gradient descent

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.741722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0a357be5-d9a2-49dd-8558-668390df0f61 · outbound

This paper cites A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:30:23.740706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 86faa8ba-363c-4dcb-a989-089fad399139 · outbound

This paper cites On the Last-Iterate Convergence of Shuffling Gradient Methods.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal On the Last-Iterate Convergence of Shuffling Gradient Methods

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:30:23.744216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 61ffd648-4fbf-4db2-8d23-132d890b040d · outbound

This paper cites Revisiting the last-iterate convergence of stochastic gradient methods.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Revisiting the last-iterate convergence of stochastic gradient methods

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.731011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e19c3644-f96d-47f9-a86a-fac7c120ad3a · outbound

This paper cites Non-asymptotic analysis of stochastic approximation algorithms for machine learning.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Non-asymptotic analysis of stochastic approximation algorithms for machine learning

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.737979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2c01f2ea-8f90-41b3-a970-8725063b6b61 · outbound

This paper cites Robust stochastic approximation approach to stochastic programming.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Robust stochastic approximation approach to stochastic programming

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.723136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2d61c199-1f46-4708-8e77-f18333834d71 · outbound

This paper cites Problem complexity and method efficiency in optimization.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Problem complexity and method efficiency in optimization

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.709678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 286c8b73-8bf1-492b-a902-f0fb7a374bc1 · outbound

This paper cites The asymptotic density of sequences.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal The asymptotic density of sequences

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.719535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7d4d6dc1-ac57-450c-be31-c570bd34928c · outbound

This paper cites Acceleration of stochastic approximation by averaging.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Acceleration of stochastic approximation by averaging

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.734334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ad5164eb-b86f-4806-9b02-7166038271d4 · outbound

This paper cites Making gradient descent optimal for strongly convex stochastic optimization.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Making gradient descent optimal for strongly convex stochastic optimization

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.713829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 358f4fdb-14da-45d8-a4d8-d7a495ee0af0 · outbound

This paper cites A stochastic approximation method.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal A stochastic approximation method

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.753565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 52438777-6c11-4529-a4a3-fd804b42c83d · outbound

This paper cites Open problem: Is averaging needed for strongly convex stochastic gradient descent? In Conference on Learning Theory, pages 47--1.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Open problem: Is averaging needed for strongly convex stochastic gradient descent? In Conference on Learning Theory, pages 47--1

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.674483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5c6a6564-73a7-483c-b91d-792af65e0f19 · outbound

This paper cites Stochastic gradient descent for non-smooth optimization: Convergence results and optimal averaging schemes.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Stochastic gradient descent for non-smooth optimization: Convergence results and optimal averaging schemes

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.594693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b851b89-0d2f-42bd-a121-9a1d2b6ab3c8 · outbound

This paper cites Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.665090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 077b539b-34c8-4316-b5d1-ce1013ff897e · outbound

This paper cites Last iterate convergence of sgd for least-squares in the interpolation regime.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Last iterate convergence of sgd for least-squares in the interpolation regime

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.669833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 90df7d6c-f675-451f-a912-b49bbdbd2f20 · outbound

This paper cites Exact convergence rate of the last iterate in subgradient methods.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Exact convergence rate of the last iterate in subgradient methods

Reference 29

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T12:30:23.747778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f9082fea-c936-4b01-b52f-04802ebea0d4 · outbound

This paper cites Solving large scale linear prediction problems using stochastic gradient descent algorithms.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Solving large scale linear prediction problems using stochastic gradient descent algorithms

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.571861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0e1f624e-113c-4f4e-bcb2-8790175b5b4b · outbound

This paper cites Anytime acceleration of gradient descent.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Anytime acceleration of gradient descent

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T09:13:04.567951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation e337a14d-a41b-47a1-b130-7f0223b7f36b · inbound

New Bounds for the Last Iterate of the Stochastic subGradient Method cites this paper.

New Bounds for the Last Iterate of the Stochastic subGradient Method Gradient Descent's Last Iterate is Often (slightly) Suboptimal

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-07-04T18:40:02.585381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9e1462eb-f937-4532-a010-5810f11c25c9 · inbound

Dangerous Liaisons of Convex Learning and Non-Affine Aggregation cites this paper.

Dangerous Liaisons of Convex Learning and Non-Affine Aggregation Gradient Descent's Last Iterate is Often (slightly) Suboptimal

Reference 231

Resolution: metadata mismatch; local_arxiv, observed 2026-06-29T18:53:52.019759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4899f82c-5462-4ba3-8c4b-3f31964622b5 · inbound

WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training cites this paper.

WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training Gradient Descent's Last Iterate is Often (slightly) Suboptimal

Reference 46

Resolution: unresolved; no resolver link, observed 2026-07-14T08:04:06.432613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.